A discrete time exact solution approach for a complex hybrid flow‐shop scheduling problem with limited‐wait constraints

We study a real‐world complex hybrid flow‐shop scheduling problem arising from a bio‐process industry. There are a variety of constraints to be taken into account, in particular zero intermediate capacity and limited waiting time between processing stages. We propose an exact solution approach for this optimization problem, based on a discrete time representation and a mixed‐integer linear programming formulation. The proposed solution algorithm makes use of a new family of valid inequalities exploiting the fact that a limited waiting time is imposed on jobs between two successive production stages. The results of our computational experiments confirm that the proposed method produces good feasible schedules for industrial instances.